TY - JOUR
T1 - Pricing American Options under Regime-Switching Model with a Crank-Nicolson Fitted Finite Volume Method
AU - Gan , Xiaoting
AU - Yin , Junfeng
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 499
EP - 519
PY - 2020
DA - 2020/06
SN - 10
DO - http://doi.org/10.4208/eajam.170919.221219
UR - https://global-sci.org/intro/article_detail/eajam/16979.html
KW - American option pricing, regime switching, fitted finite volume method, Crank-Nicolson
scheme.
AB - <p style="text-align: justify;">A new numerical method for pricing American options under regime-switching model is developed. The original problem is first approximated by a set of nonlinear partial differential equations. After that a novel fitted finite volume method for the
spatial discretisation of the nonlinear penalised system of partial differential equations
is coupled with the Crank-Nicolson time stepping scheme. It is shown that the discretisation scheme is consistent, stable, monotone and hence convergent. In order to solve
nonlinear algebraic systems, we apply an iterative algorithm and show its convergence.
Numerical experiments demonstrate the convergence, efficiency and robustness of the
numerical method.</p>